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April 6th to May 7th, 2021

This programme was interrupted due to the COVID-19 pandemic. For more information on the activities held before the intrerruption, 
General i​nformation

Dynamical systems is a wide area of research which goes beyond mathematics itself, and includes many applications. In addition, the tools are varied and come from most of the classic research lines in mathematics, such as real and complex analysis, measure theory, ergodic theory, numerical analysis and its computational implementation, topology, number theory, etc. Roughly speaking, the theory of dynamical systems consists in the rigorous study of one, several, or even infinitely many features associated to a process that depends intrinsically on parameters and that evolves when an independent variable (that we call time for obvious reasons) varies. Most of the problems in this context arise from physics (movement of celestial bodies, heat evolution in a rigid body...), biology (evolution in a structured population, neuroscience, cell growth...), economy (generational phenomena, market prices evolution...), chemistry (chemical reactions), new technologies (complex networks) or from mathematics themselves (graph theory, fractals, chaos...).

The main objects of interest in any dynamical system depending on parameters, no matter in which specific framework occurs, are the following:

  • • The phase portrait for a fixed parameter of the system, which serves to determine the future value of the system features (or system states) in the phase space based on their present values;

  • • The bifurcation diagram in the parameter space, which is meant to describe how a specific feature of the system varies as we move the parameters. In this respect it deserves particular attention the bifurcation phenomena that occur at those parameters which lie on the boundary between qualitatively different phase portraits.

 Understanding these objects is formalized into different statements or challenges depending on the context. In particular there is a preliminary division based on whether the evolution of the process is continuous (real time) or discrete (natural or integer time), but there are other relevant considerations as the dimension of the problem (i.e., number of features we wish to observe), the topology of the phase space, the type of bifurcations in the parameter space, etc. The origin of the discrete version goes back to the studies of the chaotic dynamics by A.N. Sharkovskii (1964) and T.Y. Li and J.A. Yorke (1975) for the real case, together with the works of Cayley about Newton's method (1879), the memoirs of P. Fatou and G. Julia (1920), and the notes of Orsay written by A. Douady and J.H. Hubbard (1982). Both scenarios -real and complex- show that very simple models in low dimension can exhibit extremely rich dynamics. In this context the present proposal focuses in problems related to topological and combinatorial dynamics and the description of the period set of continuous maps in graphs and trees. We also want to study the topological and analytical properties of the connected components of the Fatou set and the dynamics on their boundaries, the existence and distribution of wandering domains inside the Fatou set and the description of the parameter space and its bifurcations.

​Main activities

Weekly joint seminar:​ For the duration of the program, different dynamical systems seminars in the Barcelona area will merge into this seminar at the CRM.​

Scientific committee
​Núria Fagella​ ​Universitat de Barcelona
​Francesc Mañosas ​Universitat Autònoma de Barcelona
​Michal Misiurewiz Indiana University – Purdue University Indianapolis
​Robert Roussarie ​Université de Bourgogne
​Gwyneth Stallard ​Open University​
Peter De Maesschalck​ ​University of Hasselt​
​​Antonio Garijo​ ​Universitat Rovira i Virgili
Xavier Jarque​​ ​Universitat de Barcelona
​​​David Juher Universitat de Girona
​Boguslawa Karpinska ​Technical University of Warsaw
​Lubomir Snoha ​University of Bratislava
​Joan Torregrosa ​Universitat Autònoma de Barcelona
​Jordi Villadelprat ​Universitat Rovira i Virgili
Invited visiting researchers​​
JozefBobokCzech Technical University in Prague01/03/202028/03/2020
HenkBruinUniversity of Vienna03/02/202014/02/2020
ClaudioBuzziUniversidade Estadual Paulista02/02/202004/03/2020
PeterDe MaesschalckUniversiteit Hasselt03/02/202022/02/2020
KealeyDiasCity University of New York02/02/202022/02/2020
IgsylDomínguezPontificia Universidad Católica de Chile02/02/202027/04/2020
VasilikiEvdoridouThe Open University15/04/202030/04/2020
NuriaFagellaUniversitat de Barcelona02/02/202020/04/2020
XavierJarqueUniversitat de Barcelona02/02/202020/04/2020
DominikKwietniakJagiellonian University in Kraków15/03/202028/03/2020
KirillLazebnikCaltech University15/04/202026/04/2020
JérômeLos Université d'Aix-Marseille17/02/202031/03/2020
MichalMisiurewiczIndiana University02/02/202028/03/2020
PiotrOprochaAGH University of Science and Technology15/03/202029/03/2020
DanielPanazzoloUniversité de Haute-Alsace16/02/202001/03/2020
SalomónRebollo PerdomoUniversidad del Bío-Bío29/01/202029/02/2020
MiriamRomeroUniversidad Autónoma del Estado de Morelos03/02/202030/04/2020
RobertRoussarieUniversité de Bourgogne09/02/202022/02/2020
MitsuhiroShishikuraKyoto University01/02/202008/02/2020
LubomírSnohaMatej Bel University01/03/202029/03/2020
Bishnu HariSubediTribhuvan University02/02/202027/04/2020
JordiVilladelpratUniversitat Rovira i Virgili03/02/202026/04/2020
​​ ​​
 Further information​​
For inquiries about the programme please contact the research programme's coordinator Ms. Núria Hernandez at​

The EMS offers some travel grants to young mathematicians from less-favoured regions within the geographical area of EMS membership for presenting results at conferences or attending courses, or for research stays in foreign countries, normally up to a maximum of 900 euros in each case or 500 euros for trips within Europe.
Eligible researchers should use this online form​ in order to apply for travel grants.
The applications must be submitted by September 30th, 2020.​ 
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